Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

1997 ◽  
Author(s):  
N. Duke Perreira
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Multibody Systems ◽  
Invariant Form ◽  
Second Law ◽  
Orthogonal Projections ◽  
Gauge Invariant ◽  
Motion Equations ◽  
Newton's Second Law ◽  
Constraint Surface

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

scholarly journals Cases of integrability corresponding to the pendulummotion on the plane

2017 ◽  
Vol 21 (10) ◽  
pp. 91-113
Author(s):  
M.V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Invariant Form ◽  
Motion Equations ◽  
Plane Parallel ◽  
Free Rigid Body ◽  
Parallel Motion ◽  
Tracking Force ◽  
Similar Force

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconserva- tive force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

A New Dynamics Model of Structure-Changing Multibody Systems with Flexible Appendages

2012 ◽  
Vol 479-481 ◽  
pp. 715-719
Author(s):  
Zheng Ning Yu ◽  
Wen Long Li ◽  
Yu Shan Zhao
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Rigid Body ◽  
Multibody Systems ◽  
Engineering Application ◽  
Body System ◽  
Dynamics Model ◽  
Traditional Methods ◽  
New Approach ◽  
Flexible Appendages

According to engineering requirements, structure of multibody systems would change and lead to obvious modifications in dynamics model obtained by traditional methods. In this paper, an existing method for rigid body systems with changing structures is extended to systems with flexible appendages, which is more common in engineering. Application of the new generalized approach to a typical 4-body system is actualized. Numerical simulation is carried out and results are the same as theoretical analysis, which indicate the availability and applicability of the new approach.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Feeling Newton’s Second Law

2019 ◽  
Vol 57 (2) ◽  
pp. 88-90 ◽  
Author(s):  
Vincent P. Coletta ◽  
Josh Bernardin ◽  
Daniel Pascoe ◽  
Anatol Hoemke
Keyword(s):  
Second Law ◽  
Newton's Second Law

Scootin' with Newton: Teaching Newton's Second Law Using Motion

Strategies ◽  
2002 ◽  
Vol 16 (2) ◽  
pp. 7-11
Author(s):  
Deborah A. Stevens-Smith ◽  
Shelley W. Fones
Keyword(s):  
Second Law ◽  
Newton's Second Law

A dynamic method to measure the shear strength of snow

2010 ◽  
Vol 56 (196) ◽  
pp. 333-338 ◽  
Author(s):  
Tsutomu Nakamura ◽  
Osamu Abe ◽  
Ryuhei Hashimoto ◽  
Takeshi Ohta
Keyword(s):  
Shear Strength ◽  
Strain Rate ◽  
Reasonable Agreement ◽  
Dynamic Method ◽  
Second Law ◽  
Snow Density ◽  
Newton's Second Law

AbstractA new vibration apparatus for measuring the shear strength of snow has been designed and fabricated. The force applied to a snow block is calculated using Newton’s second law. Results from this apparatus concerning the dependence of the shear strength on snow density, overburden load and strain rate are in reasonable agreement with those obtained from the work of previous researchers. Snow densities ranged from 160 to 320 kg m−3. The overburden load and strain rate ranged from 1.95 × 10−1to 7.79 × 10−1kPa and 2.9 × 10−4to 9.1 × 10−3s−1respectively.

Sign in / Sign up

Export Citation Format

Share Document